Traces of the Nevanlinna class on discrete sequences

Andreas Hartmann (1) , X Massaneda (2) , A Nicolau (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Departament de Matemàtica Aplicada i Anàlisi [Barcelona]
3 UAB - Departament de Matemàtiques [Barcelona]

We show that a discrete sequence $\Lambda$ of the unit disk is the union of $n$ interpolating sequences for the Nevanlinna class $N$ if and only if the trace of $N$ on $\Lambda$ coincides with the space of functions on $\Lambda$ for which the divided differences of order $n - 1$ are uniformly controlled by a positive harmonic function.

Mots clés: Divided differences; Interpolating sequences; Nevanlinna class

Domaines: Variables complexes [math.CV]

Andreas Hartmann, X Massaneda, A Nicolau. Traces of the Nevanlinna class on discrete sequences. Complex Analysis and Operator Theory, 2018, 12 (8), pp.1945-1958. ⟨hal-01467658⟩